Graph from cyclingincities / Safety & Travel Mode.
Exposure-based Traffic Crash Injury Rates by Mode of Travel in British Columbia; a 2013 Kay Teschke, et al published article in Can J Public Health (full text freely available).
5 Reasons Why Riding a Bike is Safe / Teschke. Has a slick info-graphic with same data as above “Bicycling is similar in safety to driving and walkin. If you want to maximize safety alone, then transit is the travel choice you should make”.
Note that this is exact same title and conclusions as a study published in 2007…
Relative to passenger vehicle occupants, motorcyclists, bicyclists, and pedestrians are 58.3, 2.3, and 1.5 times, respectively, more likely to be fatally injured on a given trip. Bus travel is the safest travel mode
The Risk of Dying Doing What We Love published a neat chart that compares a broad range of activities; it uses commercial airline travel as the benchmark and attempts to list an exposure (by time) adjusted risk value; i.e. driving is 4X as dangerous, bicycling is 8X as dangerous (i.e. cycling is twice as dangerous as driving in a car). Motorcycling comes out as 100X, i.e. 25 times worse than driving in a car, in line with what Teschke published, above.